Trees pruned correctly will seal over to prevent insect and disease from having an opening. These pictures represent the process. The pruning cut is made outside the branch collar which is a swollen area where the branch and trunk meet. Now is a fine time to manage your trees and make limb removal decisions.
Removal of a limb requiring a pruning saw is removed in three steps. The first cut is made under the limb, 12 inches from the trunk. Cut a third of the way through the trunk. The second cut is made from the top down 14 inches from the trunk until the limb snaps off. The final cut removes the remaining portion of the limb. This final cut is made outside the branch collar and leaves mostly a circular wound.
For good information on pruning, go to http://hort.ifas.ufl.edu/woody/pruning.shtml